where
\(\tilde{\omega }_{P_{\infty _+}, P_{\infty _-}}^{(3)}=a~z^{n}dz/y(P)\)  (cf.(F.53) [1]})
and
\(\begin{split}& \underline{\hat{\beta }}_{Q_0}:\mathrm {Sym}^n(\mathcal {K}_n \setminus \lbrace P_{\infty _+}, P_{\infty _-}\rbrace ) \rightarrow \mathbb {C}^n, \\& \mathcal {D}_{\underline{Q}} \mapsto \underline{\hat{\beta }}_{Q_0}(\mathcal {D}_{\underline{Q}})=\sum _{j=1}^n \underline{\widehat{B}}_{Q_0}(Q_j),\quad \underline{Q}=\lbrace Q_1,\ldots ,Q_n\rbrace \in \mathrm {Sym}^n( \mathcal {K}_n \setminus \lbrace P_{\infty _+}, P_{\infty _-}\rbrace ),\end{split}\) 
